2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217032We show that for stochastic dynamical systems out of equilibrium the violation of the fluctuation-dissipation equality is bounded by a function of the entropy production. The result applies to a much wider situation than `near equilibrium', comprising diffusion as well as glasses and other macroscopic systems far from equilibrium. For aging systems this bounds the age-frequency regimes in which the susceptibilities satisfy FDT in terms of the rate of decay of the H-function, a question intimately related to the reading of a thermometer placed in contact with the system.4 pages, RevTex; formula and reference added plus various minor changes in the textStatistical MechanicsChaotic DynamicsHigh Energy Physics - Theorytext